基于动力松弛法的松弛索杆体系找形分析

索杆张力结构施工成形分析需要解决一个松弛态索杆系统的平衡形态求解问题,该问题可归结为一个给定构件原长的受荷索杆机构系统的找形问题。文中利用动力松弛法进行该类松弛索杆体系的找形分析。由于不建立刚度矩阵,避免了体系几何不稳定性所引起的刚度矩阵奇异问题。该方法采用悬链线索单元模型,可以考虑索大垂度效应。文中还推导了反映索原长和内力之间关系的悬链线索单元协调方程。通过一个正交松弛索网算例分析,考察了该找形方法的计算精度和收敛性。最后还模拟了一个索穹顶的施工成形过程,表明了该找形方法用于索杆张力结构施工成形分析的有效性。

Form finding of slack cable-bar assembly by dynamic relaxation method

The erection simulation of cable-strut tensile structures involves equilibrium state analysis of a slack cable-bar assembly.This issue is clarified as a kind of form-finding problem for a loaded cable-bar mechanism system with prescribed unelongated member lengths.The dynamic relaxation method is accepted to solve this unconventional form-finding problem.Since no stiffness matrix is established in this method,difficulties caused by matrix singularity due to the geometrical instability of such mechanism assembly can be avoided in numeric computation.Catenary element is adopted to exactly consider the large-sag effect of slack cable.A new compatible equation of catenary cable element,which reflects the relationship between unelongated cable length and its tensile force,is put forward.An orthogonal slack cable net is employed as a numeric example to verify the accuracy and convergency of this method.Numeric simulation of erection process of a cable dome is further carried out,and shows the validity of this method for the erection simulation analysis of cable-strut tensile structures.